Orthogonal variable spreading factor (OVSF) codes have been proposed as the channelization codes used in the wideband CDMA access technology of IMT-2000. OVSF codes have the advantages of supporting variable bit rate services, which is important to emerging multimedia applications. The objective of OVSF code assignment algorithm is to minimize the probability of code request denial due to inappropriate resource allocation. In this paper, we propose an efficient OVSF code assignment scheme that utilizes multiple RAKE combiners in user equipments. Our approach finds in constant time all feasible codewords for any particular request, trying to minimize both rate wastage and code fragments. When working together with an independent code replacement scheme, our approach has the same code request denial rate as previous work but has lower code management overhead. If code replacement is not used, our approach still has a bit of improvement on request denial rate.